On the Classification of Bulk and Boundary Conformal Field Theories

TL;DR

This paper revisits the classification of rational conformal field theories by analyzing boundary conditions through Cardy's equation, linking boundary solutions to bulk properties and fusion algebra representations.

Contribution

It provides a complete classification of boundary conditions in rational conformal field theories and connects boundary solutions to bulk characteristics.

Findings

Complete solutions to Cardy's equation identify admissible boundary conditions.

Boundary conditions correspond to integer-valued fusion algebra representations.

Results offer insights into bulk properties from boundary analysis.

Abstract

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties.